Mobility Model By Lewis
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Transcript of Mobility Model By Lewis
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(1) Brief Survey of Mobility Modelsfor Ad Hoc Networks and WLANs
(2) A Mobility Model for Both Long-term Mobility Characteristics and
Timed Location Prediction in WLANsPresented by Jong-Kwon Lee
November 11, 2005
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Random Walk Model Originally proposed to emulate the unpredictable
movement of particles in physics (referred to asBrownian Motion)
Each node moves from its current location to anew location by randomly choosing a directionand speedin which to travel.
For every interval t, randomly choose
New Speed
[vmin, vmax] New Direction (0, 2]
No pause time
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Random Waypoint Model Widely used in mobile ad hoc network research
Behavior of each node
selects a random point in the simulation area as its destination,and a speedVfrom an input range [vmin, vmax].
Moves to its destination at its chosen speed.
When the node reaches its destination, it rests for some pausetime.
After this pause time, it selectsa new destination and speed,
and repeats the process.
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Reference Point GroupMobility Model
A mobility model with spatial dependency
Represents the random motion of a group of mobilenodes as well as the random motion of each individualnode within the group
Group leader
Movement of a group leader attime t:
Group members
Mobility is assigned with areference point that follows thegroup movement:
t
groupV
t
it
group
t
iRMVV
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Obstacle Mobility Model(MobiCom03)
Nodes move around pre-defined (rectangle) obstacles(e.g. buildings)
Voronoi diagram is used to determine the path of mobilenodes.
Planar graph whose edges are line segments that are equidistantfrom two obstacle corners
A variation of Random Waypoint model
The environment limits the trajectories of
mobile nodes to the Voronoi graph. Obtain the shortest path between a nodes
current location and its destination.
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Empirical Model Weighted Waypoint (WWP) model
Based on surveys from sampled respondents on USC campusduring 4 weeks
Destinations are not randomly picked with the same weight
across the simulation area. The parameters of a mobility model (e.g. pause time) are
location-dependent and time-dependent.
Topology of virtual-campus5-state Markov model for mobile nodetransition between categories
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WLAN Mobility Model(Infocom05)
Uses real-life mobility characteristics extractedfrom WLAN traces to generate mobility scenarios.
load environment description
for every simulated node do
time := 0
while time < t_sim do
call PS{select next destination}call PT{generate timing}
move to next destinationtime := time+current_session
end while
end for
Algorithm used by the WLAN mobilitymodel to generate node trajectories
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Model T (MobiCom05)
Model only for spatial registration patterns
Develop a model as a set of equations thatcharacterize the salient features of the (training)
data set No. and distribution of clusters
No. of popular APs in a cluster size C
Intra-cluster transition probability
Intra-cluster trace length
Inter-cluster transition probability
Inter-cluster trace length
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Motivation
Recent studies on characterization of usermobility and network usage in WLANs
Few studies on how the user mobility is
correlated in time (daily, weekly, monthly timescales).
Existing prediction models for user
locations in WLANs Predict only the next location w/o time
information
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Semi-Markov Mobility Model Continuous-time Markov chain (CTMC)
can characterize users state transitions as well as thesojourn times spent in each state.
However, the sojourn time characteristics ofusers in campus-like WLAN do not follow anexponential distribution.
Semi-Markov Processes Generalization of Markov processes with arbitrary
distributed sojourn times.
Can be used for obtaining both steady-statedistribution and transient distribution
characterize long-term usage of network resource +
timed location prediction with one model!
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Semi-Markov Mobility Model
Discrete state space S={1, , m}
Markov renewal process {(Xn, Tn): n0}
(Time homogeneous) semi-Markov process
Transition prob. from i to j
Sojourn time distribution instate i when the next state is j
Transition prob. matrix of the embedded Markov chain
Sojourn time distribution instate i regardless of the next state
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Steady-state User Distributionover APs
~D
noOFF
During 11/1/2003~2/29/2004
786 active users
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Similarity of Mobility Patternsbetween Different Periods
Use ofsimilarity measuresto check thecorrelation of the mobility behavior Cosine distance(= correlation coefficient)
: a pattern similarity measure
* 0 sim(p,q) 1sim(p,q) = 1 Identical Pattern
qpqp
qp
qpqpsim
m
i i
m
i i
m
i ii
1
2
1
2
1),(
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Monthly Correlation 1 month = 4 weeks 8 months (11/2/2003 ~ 6/12/2004)
More similar between consecutive periods
3/21/2004~4/17/2004
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Weekly Correlation 14 weeks (2/1/2004~5/8/2004)
3/21/2004~4/17/2004
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Daily Correlation For each day of week (Sunday, Monday, , Saturday)
8 weeks (11/2/2003~12/27/2003)
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Different User Groups
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Ping-Pong Phenomena Ping-pong transition: for APs i, j, and k,
(ijij) or (ijki)
For each user, Ping-pong ratio = [# of ping-pong transitions] / [# of all transitions]
For 786 users, Average ping-pong ratio = 0.40
Median = 0.38
Ping-pong happens quite oftenand should not be ignored !
=> The transition probability and residence time characteristics at each APwith the original association patterns can distortthe actual mobilitybehavior.
CDF
(cumul
ativefractionofusers)
Ping-pong ratio
M bili Ch D Pi
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Mobility Change Due to Ping-Pong Phenomena
Elimination of ping-pong transitions from theoriginal association history of each user Identify a sequence of ping-pong transitions
Cluster the states (i.e. APs) in the sequence of the
ping-pong transitions into an Aggregate State (AS) Replace the sequence of the ping-pong transitions
with just one transition to the dominant AP with whichthe user has mostly associated among the APs in the
same ASex) a->1->4->1->4->b=> a->1->b if 1 is dominant in AS={1,4}
a->4->b if 4 is dominant in AS={1,4}
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Mobility from Corrected Data(after Elimination of Ping-Pong)
~D
noOFF
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Mobility from Original Data
~D
noOFF
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Change in Residence Time
Ti d P di ti f U
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Timed Prediction of UserLocation
Transient behavior of semi-Markov model
Numerical solution: discretize by t = kh
Ti d P di ti f U
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Timed Prediction of UserLocation
Predict users location at every k time steps k
ij
nk(n-1)k (n+1)k
Ti d P di ti f U
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Timed Prediction of UserLocation: Results
h = 600, K = 12, Tp = 1800
A li ti M bilit
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Application: Mobility-awareLoad Balancing in WLAN
Lets take advantage of ping-pong phenomena. Rationale: APs in the same AS has served in turn the user with
the acceptably high SNR.
Basic idea of load balancing over APs Assume the load at each AP is the number of users at the AP.
(We may later extend this to the case of traffic amount at eachAP.)
Move users at overloaded APs to a lightly loaded AP in the sameAS.
Balance Index:
where m: # of APs, Li: load at AP i
= 1 : All Lis have the same value. 1/n : Heavily unbalance.
22
iiLmL
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Overview of the Mobility-awareLoad Balancing Algorithm
Incorporating timed location prediction Can predict future load distribution.
Can avoid load unbalance in advance.
Use a 1xm bit vector AC to control the association of users to APs(m: # of APs)
Initially, AC(i) = 1 for all AP i If the load at AP i is predicted to be greater than a thresholdL, AC(i)
0.
AC(i) is reset to 1 if the load at AP i is underL (either expectedly oractually).
When a user moves to a new location, First checks the AC bit corresponding to the AP having highest signal
strength.
If it is 0 (i.e. it is overloaded), the user tries to associate to alternativeAPs in the same AS as that AP.
If the overloaded AP belongs to no AS, or there are no alternative APshaving sufficient signal strength, the user is allowed to associate to theoverloaded AP.
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Simulation Results Total users = 786, OFF users = 509, Active users = 277
Original distribution : Balance Index = 0.180823 with max load = 9 at AP 361
After load balancing : Balance Index = 0.327917 with max load = 3 at AP 373
Sim lation Res lts Mo e
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Simulation Results: MoreActive Users
Total users = 786, OFF users = 201, Active users = 585 (OFF users artificially reduced)
Original distribution : Balance Index = 0.284616 with max load = 12 at AP 361
After load balancing : Balance Index = 0.506377 with max load = 4 at AP 275